Journal of Convex Analysis 16 (2009), No. 1, 187--210
Copyright Heldermann Verlag 2009
Nondifferentiable Multiplier Rules for Optimization Problems with Equilibrium Constraints
N. Movahedian
Dept. of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran
Soghra Nobakhtian
Dept. of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran
nobakht@math.ui.ac.ir
We consider a mathematical program with equilibrium constraints (MPEC). First we obtain a Lagrange multiplier rule based on the linear subdifferential involving equality, inequality and set constraints. Then we propose new constraint qualifications for M-stationary condition to hold. Finally we establish the Fritz John and Karush-Kuhn Tucker M-stationary necessary conditions for a nonsmooth (MPEC) based on the Michel-Penot subdifferential.
Keywords: Optimization problems, necessary optimality conditions, constraint qualification, nonsmooth analysis.
MSC: 90C30, 90C46, 49J52
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